different ways to solve division problems

• PRO Courses Guides New Tech Help Pro Expert Videos About wikiHow Pro Upgrade Sign In
• EDIT Edit this Article
• EXPLORE Tech Help Pro About Us Random Article Quizzes Request a New Article Community Dashboard This Or That Game Popular Categories Arts and Entertainment Artwork Books Movies Computers and Electronics Computers Phone Skills Technology Hacks Health Men's Health Mental Health Women's Health Relationships Dating Love Relationship Issues Hobbies and Crafts Crafts Drawing Games Education & Communication Communication Skills Personal Development Studying Personal Care and Style Fashion Hair Care Personal Hygiene Youth Personal Care School Stuff Dating All Categories Arts and Entertainment Finance and Business Home and Garden Relationship Quizzes Cars & Other Vehicles Food and Entertaining Personal Care and Style Sports and Fitness Computers and Electronics Health Pets and Animals Travel Education & Communication Hobbies and Crafts Philosophy and Religion Work World Family Life Holidays and Traditions Relationships Youth
• Browse Articles
• Learn Something New
• Quizzes Hot
• This Or That Game
• Train Your Brain
• Explore More
• Support wikiHow
• About wikiHow
• Log in / Sign up
• Education and Communications
• Mathematics
• Multiplication and Division

How to Do Division

Last Updated: January 14, 2024 Fact Checked

This article was co-authored by Grace Imson, MA and by wikiHow staff writer, Christopher M. Osborne, PhD . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 520,538 times.

Division is one of the 4 major operations in arithmetic, alongside addition, subtraction, and multiplication. In addition to whole numbers, you can divide decimals, fractions, or exponents. You can do long division or, if one of the numbers is a single digit, short division. Start by mastering long division, though, because it is the key to the entire operation.

Long Division

• Sample problem #1 (beginner): 65 ÷ 5 . Place the 5 outside the division bar, and the 65 inside it. It should look like 5厂65 , but with the 65 underneath the horizontal line.
• Sample problem #2 (intermediate): 136 ÷ 3 . Place the 3 outside the division bar, and the 136 inside it. It should look like 3厂136 , but with the 136 underneath the horizontal line.

• In sample problem #1 ( 5厂65 ), 5 is the divisor and 6 is the first digit of the dividend (65). 5 goes into 6 one time, so place a 1 on the top of the divisor bar, aligned above the 6.
• In sample problem #2 ( 3厂136 ), 3 (the divisor) does not go into 1 (the first digit of the dividend) and result in a whole number. In this case, write a 0 above the division bar, aligned above the 1.

• In sample problem #1 ( 5厂65 ), multiply the number above the bar (1) by the divisor (5), which results in 1 x 5 = 5 , and place the answer (5) just below the 6 in 65.
• In sample problem #2 ( 3厂136 ), there is a zero above the division bar, so when you multiply this by 3 (the divisor), your result is zero. Write a zero on a new line just below the 1 in 136.

• In sample problem #1 ( 5厂65 ), subtract the 5 (the multiplication result in the new row) from the 6 right above it (the first digit of the dividend): 6 - 5 = 1 . Place the result (1) in another new row right below the 5.
• In sample problem #2 ( 3厂136 ), subtract 0 (the multiplication result in the new row) from the 1 right above it (the first digit in the dividend). Place the result (1) in another new row right below the 0.

• In sample problem #1 ( 5厂65 ), drop the 5 from 65 down so that it’s beside the 1 that you got from subtracting 5 from 6. This gives you 15 in this row.
• In sample problem #2 ( 3厂136 ), carry down the 3 from 136 and place it beside the 1, giving you 13.

• To continue 5厂65 , divide 5 (the dividend) into the new number (15), and write the result (3, since 15 ÷ 5 = 3 ) to the right of the 1 above the division bar. Then, multiply this 3 above the bar by 5 (the dividend) and write the result (15, since 3 x 5 = 15 ) below the 15 under the division bar. Finally, subtract 15 from 15 and write 0 in a new bottom row.
• Sample problem #1 is now complete, since there are no more digits in the divisor to carry down. Your answer (13) is above the division bar.

• For 3厂136 : Determine how many times 3 goes into 13, and write the answer (4) to the right of the 0 above the division bar. Then, multiply 4 by 3 and write the answer (12) below the 13. Finally, subtract 12 from 13 and write the answer (1) below the 12.

• For 3厂136 : Continue the process for another round. Drop down the 6 from 136, making 16 in the bottom row. Divide 3 into 16, and write the result (5) above the division line. Multiply 5 by 3, and write the result (15) in a new bottom row. Subtract 15 from 16, and write the result (1) in a new bottom row.
• Because there are no more digits to carry down in the dividend, you’re done with the problem and the 1 on the bottom line is the remainder (the amount left over). Write it above the division bar with an “r.” in front of it, so that your final answer reads “45 r.1”.

Short Division

• In order to do short division , your divisor can't have more than one digit.
• Sample problem: 518 ÷ 4 . In this case, the 4 will be outside the division bar, and the 518 inside it.

• In the sample problem, 4 (the divisor) goes into 5 (the first digit of the dividend) 1 time, with a remainder of 1 ( 5 ÷ 4 = 1 r.1 ). Place the quotient, 1, above the long division bar. Place a small, superscript 1 beside the 5, to remind yourself that you had a remainder of 1.
• The 518 under the bar should now look like this: 5 1 18.

• In the sample problem, the number formed by the remainder and the second number of the dividend is 11. The divisor, 4, goes into 11 twice, leaving a remainder of 3 ( 11 ÷ 4 = 2 r.3 ). Write the 2 above the division line (giving you 12) and the 3 as a superscript number beside the 1 in 518.
• The original dividend, 518, should now look like this: 5 1 1 3 8.

• In the sample problem, the next (and final) dividend number is 38—the remainder 3 from the previous step, and the number 8 as the last term of the dividend. The divisor, 4, goes into 38 nine times with a remainder of 2 ( 38 ÷ 4 = 9 r.2 ), because 4 x 9 = 36 , which is 2 short of 38. Write this final remainder (2) above the division bar to complete your answer.
• Therefore, your final answer above the division bar is 129 r.2.

Dividing Fractions

• Your problem might be, for example, 3/4 ÷ 5/8 . For convenience, use horizontal instead of diagonal lines to separate the numerator (top number) and denominator (bottom number) of each fraction.

• In the sample problem, reverse 5/8 so the 8 is on top and the 5 is on the bottom.

• For example: 3/4 x 8/5 .

• In this case, the numerators are 3 and 8, and 3 x 8 = 24 .

• The denominators are 4 and 5 in the sample problem, and 4 x 5 = 20 .

• In the sample problem, then, 3/4 x 8/5 = 24/20 .

• 24: 1, 2, 3, 4 , 6, 8, 12, 24
• 20: 1, 2, 4 , 5, 10, 20
• 24/20 = 6/5 . Therefore, 3/4 ÷ 5/8 = 6/5

• In the sample problem, 5 goes into 6 one time with a remainder of 1. Therefore, the new whole number is 1, the new numerator is 1, and the denominator remains 5.
• As a result, 6/5 = 1 1/5 .

Dividing Exponents

• As a beginner, start with a sample problem in which both numbers with exponents already have the same base—for instance, 3 8 ÷ 3 5 .

• In the sample problem: 8 - 5 = 3 .

• Therefore: 3 8 ÷ 3 5 = 3 3 .

Dividing Decimals

• For the example 65.5 ÷ 0.5 , 0.5 goes outside the division bar, and 65.5 goes inside it.

• In the sample problem, you only need to move the decimal point over one spot for both the divisor and dividend. So, 0.5 becomes 5, and 65.5 becomes 655.
• If, however, the sample problem used 0.5 and 65.55, you’d need to move the decimal point 2 places in 65.55, making it 6555. As a result, you’d also have to move the decimal point in 0.5 2 places. To do this, you’d add a zero to the end and make it 50.

• In the sample problem, the decimal in 655 would appear after the last 5 (as 655.0). So, write the decimal point above the division line right above where that decimal point in 655 would appear.

• Divide 5 into the hundredths digit, 6. You get 1 with a remainder of 1. Place 1 in the hundredths place on top of the long division bar, and subtract 5 from 6 below the number six.
• Your remainder, 1, is left over. Carry the first five in 655 down to create the number 15. Divide 5 into 15 to get 3. Place the three above the long division bar, next to the 1.
• Carry down the last 5. Divide 5 into 5 to get 1, and place the 1 on top of the long division bar. There is no remainder, since 5 goes into 5 evenly.
• The answer is the number above the long division bar (131), so 655 ÷ 5 = 131 . If you pull out a calculator, you’ll see that this is also the answer to the original division problem, 65.5 ÷ 0.5 .

Practice Problems and Answers

Community Q&A

You Might Also Like

• ↑ https://www.mathsisfun.com/long_division.html
• ↑ https://www.k5learning.com/blog/step-step-guide-long-division
• ↑ https://www.bbc.co.uk/bitesize/topics/znmtsbk/articles/zqpddp3
• ↑ http://www.mathsisfun.com/fractions_division.html
• ↑ https://www.ck12.org/arithmetic/divide-fractions/lesson/Quotients-of-Fractions-MSM6/?referrer=concept_details
• ↑ http://www.mathsisfun.com/algebra/variables-exponents-multiply.html
• ↑ https://www.mathsisfun.com/dividing-decimals.html
• ↑ https://www.bbc.co.uk/bitesize/topics/zh7xpv4/articles/zwdc4xs

About This Article

To do simple division, think about how many times one number can go into another number. For example, 6 ÷ 2 is 3, because 3 goes into 6 two times. For larger numbers, it's helpful to spend time reviewing the multiplication tables. To do long division, write the number you want to divide under the division bar, and place the number you want to divide by outside of the bar. For example, if you want to calculate 72 ÷ 3, place 72 under the division bar and 3 outside of it. Then, calculate how many times 3 goes into the first number under the division bar. In this case, you’re calculating how many times 3 goes into 7. The answer is 2, with 1 left over. Write the number 2 above the bar, and the remainder – in this case, 1 – below the 7. Then, if there are any numbers left under the division bar, bring them down to the same row as the remainder. So in this case, you’d write a 2 beside the 1 to get 12. Then, repeat the process: how many times does 3 go into 12? In this example, 3 goes into 12 four times, so you’d write 4 on the line above the problem, beside the other numbers. Therefore, 72 ÷ 3 = 24. If you want to learn how to divide fractions, keep reading the article! Did this summary help you? Yes No

• Send fan mail to authors

Reader Success Stories

Did this article help you?

Cori Landerson

Apr 22, 2017

Sep 12, 2023

Nov 2, 2022

Featured Articles

Trending Articles

Watch Articles

• Terms of Use
• Privacy Policy
• Do Not Sell or Share My Info
• Not Selling Info

wikiHow Tech Help Pro:

Level up your tech skills and stay ahead of the curve

• Teaching Resources
• Privacy Policy

Division Strategies: Building a Strong Foundation for Mathematical Proficiency

Mathematics can sometimes feel like a tricky puzzle, especially when it comes to division strategies. Many students find division challenging and overwhelming, but fear not! There are fantastic division strategies that can make this math operation a whole lot easier and even enjoyable.

We’re going to explore some key division strategies that will help you build a strong foundation for math success. Whether you’re a parent or teacher searching for tools to support young learners, we’ve got you covered.

We’ll start with the basics and gradually move on to more advanced approaches. By mastering these division strategies, students can not only solve division problems accurately but also develop critical thinking skills, problem-solving abilities, and a deeper understanding of number relationships. These strategies lay the groundwork for more advanced mathematical concepts and serve as stepping stones toward mathematical fluency.

Division Strategies

Below you will see five different division math strategies that your students might use.  Each student will be in a different spot with their math strategies. For example, some students need the concrete/manipulatives and equal groups will be best for them.  Other students might be ready for repeated subtraction or related facts.  Students can use a variety of strategies and will move through them at different rates when they are ready. I highly recommend letting them explore these strategies first so they understand the concept of division before having them memorize their division facts.

Equal Groups

Draw out circles for the number of groups that you have. This problem is 18 divided into 6 groups and we need to figure out how many are in each group. Then, in each group put 1 dot until you get to 18. Finally, students will count how many are in each circle/group. Students can count these in a variety of ways. Some students may count by 1s, 2s, 4s. I recommend having them write the number they are on below each circle to help them keep track. After counting by 1’s, the students came to the answer of 3.

Bar Diagram

This is very similar to equal groups just a different way to visually represent the problem. Students will draw out a rectangular bar and then divide that bar into 6 groups. Then, they will put one in each group until they get to the total number they started with – 18. Then, count how many are in each group. Some students might also like the visual with the number 3 instead of the dots depending on where they are in their understanding of division.

Repeated Subtraction

Repeated subtraction is exactly like repeated addition except you’re subtracting. For this problem, students would start at 18 and would start subtracting by 6 until they get to 0. For example – 18-6 = 12, 12-6 = 6, and then 6-6 = 0. They had to subtract 6 – 3 different times so 3 is the quotient.

Empty Number Line

The empty number line division strategy is similar to repeated subtraction just a different way of visualizing it. For students who like to use empty number lines in math, this strategy might be the best one for them. Students start by drawing their empty number line and placing the starting number 18 on the far right. Then, they subtract 6 until they get to 0. They had to subtract 6 – 3 times so the answer is 3.

Related Facts

For math students who have a solid understanding of multiplication and are ready for a more abstract strategy – related facts might work for them. For this strategy, students turn the division problem 18/6 = ___ into a multiplication problem 6 x __ = 18. So now they are trying to figure out what they would multiply by 6 to get to 18 and then using that related fact to solve the division problem.

Division Strategies Exit Ticket FREEBIE

Grab this FREE set of exit tickets that will provide your math students with a chance to practice and demonstrate their division strategies. Includes 3 half-page questions that make a great exit ticket, independent practice, or formative assessment. Click HERE for your Division Strategies FREEBIE.

For more info…

Division Tip for Conceptual Understanding

Differentiated Division Word Problems

Share this:

• Click to share on Twitter (Opens in new window)
• Click to share on Facebook (Opens in new window)

You Might Also Like

Five for friday – july 22, teaching about money.

Football Room Transformation

No comments, leave a reply cancel reply.

I accept the Privacy Policy

Notify me of follow-up comments by email.

Notify me of new posts by email.

Division in Math

Division is a math superpower that breaks down a whole — whether you’re cutting a pizza or divvying up some candy!

Author Christina Levandowski

Expert Reviewer Jill Padfield

Published: August 24, 2023

• Key takeaways
• Division is an opposite game – If you multiply numbers, you can “undo” them using division. It’s multiplication’s opposite function! 
• There’s a few signs to look for – There are three main symbols for division.
• You won’t always get “even Stevens” – Sometimes, you’ll have a little left over. That leftover number is known as the “remainder.”

Table of contents

What is division?

Common symbols and terminology, properties of division, how to divide in 6 easy steps, what is long division, working with remainders.

• Let’s practice together!

Practice problems

Division is one of the most important math skills you’ll practice, helping you to undo multiplication problems or break off parts of a “whole.” We know it looks complicated, but it really isn’t! You just need to know what signs to look for that tell you when division is needed. 

Like addition and subtraction, division uses a few special terms and symbols. Knowing these can help you to work out your problems quickly and correctly. 

We know it sounds complicated right now — but with a little practice and this handy guide, you’ll be flying through your math homework in no time!

Division is a process in math that lets you break down a number into multiple, equal parts. Sometimes, you can cut everything down into whole number parts, and, sometimes, you’ll be left with a little leftover, giving you a decimal or fraction for an answer rather than a whole number. 

You’ll often see division problems vertically, like this:

It can also be written horizontally: 10 ÷ 2, as 10/2 , or using a division bar: 2 ⟌ 10.

No matter how you see it, though, the use for it is always the same. You’re breaking down a number or quantity into smaller pieces. 

Let’s take a look at some key terms that’ll help you build your division skills.

Division is a simple mathematical operation, but there are still a few terms to know to help you find the correct solution. 

Here are the terms you need to know to solve division equations with ease:

➗ — This is known as a division sign, and it tells you that a number needs to be broken down into multiple pieces. 

⟌ — This is the division bar, and it also means to divide. On the outside of the bar, you’ll see the number determining how many pieces are needed from the whole (the divisor), and the dividend on the inside, which is what you’ll be dividing. The answer goes on the top of the bar. 

∕ — This is known as the division slash. Generally, the divisor comes first, and the dividend will appear second.

Important vocabulary

• Divisor – The divisor is the number that is determining how many pieces are needed from the whole. For example: in 15 ÷ 3, three would be the divisor. It’s also the number located outside of the bracket when you see a division bar.
• Dividend – The dividend is the number that’s being divided, and it’s found inside the division bar.
• Quotient – The quotient is your answer, which goes after the equals (=) sign or on the top of the division bar.
• Remainder – In some cases, you’ll have a remainder — which means that the divisor can’t be equally divided into the dividend. The remainder is written to the side of your equation next to the division bar.

Anytime you see the word “property” in math, know that it’s just a rule to remember as you work through your groups of problems. Here are some of the most important properties of division that you need to know: 

• The Division By 1 Property:  If a number is divided by 1, the quotient will always be the original number. 
• The Division By Itself Property: If a number is divided by itself, the quotient will always be 1. 
• The Division By 0 Property: If a number is divided by 0, it’s “undefined” and cannot be solved. 
• The Division Of 0 By (Any) Number Property: If a 0 value is divided by any number, you’ll have 0 as your quotient.

Knowing these helpful properties can help you to do basic operations (like division) confidently. Remember — these are division facts, so these properties will always be true…no matter what problem you’re working to find the quotient to!

Now that you know the terms and properties of your division operation, it’s time to practice your skills. Let’s work the problem below together. 

1. Prepare your equation

We know that the problem above can feel overwhelming — so we want to take this moment to remind you that what we’re doing is breaking down a number into smaller numbers (or smaller groups of numbers). 

First things first, we have to prepare the equation. Feel free to keep it horizontal,  write it vertically, or use a division bar if you’d like. Use whatever method you feel comfortable with. 

Remember: The dividend (15) belongs inside the division bar if you choose to use that method. 

2. Start with the first digit of the dividend from the left

As we begin to divide, we need to start from the first digit from the left (in this case, 1) and ask ourselves: Does the divisor (3) go into 1 at least once? 

The answer here is “no,” so we will then evaluate the first AND second integer (making 15) as a dividend. 

We ask again: Does the divisor (3) go into 15 at least once? 

Now, the answer is “yes” — we just have to count how many times 3 can go into 15, starting our division process.* 

*NOTE: You can do this by using basic arithmetic operations (such as multiplication) to “undo” the problem (i.e., 3 x ? = 15) or counting by threes until you reach 15. 

In our case, 3 goes into 15 a total of five times.

3. Divide it by the divisor and write the answer on top as the quotient

Now that we know that 15 ÷ 3 = 5, it’s time to write it into our equation. Go ahead and write 5 behind the equals sign or standing tall at the top of your division bar. 

4. Subtract the product of the divisor and the digit written in the quotient from the first digit of the dividend

Now, we have to check our work. We have to ask ourselves: What is 5 x 3? Does it equal our dividend? If it does, you’re golden — you’ve done it! 

Do the multiplication, and then subtract your product to ensure that there’s no other steps remaining (like you’d see in the case of a remainder). 

In our example, 15 – 15 = 0…so no remainder or further action is needed.

5. Bring down the next digit in the dividend (if possible)

In other problems, if you did have a three or four digit dividend, you might need to bring down the next digit in the dividend, and determine if your divisor divides that number cleanly. 

You would then repeat the division process, putting your answer over the third or “next” place above the division bar as part of the quotient. 

Next, yo would repeat step 4 to determine if more steps in the division process are needed.

In our example, we don’t have to do this, so we will leave it as is. Good work!

Congratulations! You just broke a large number down into equal, separate parts. It’s time to repeat the process for your other problems. 

Long division is a form of division that’s used to break down larger numbers and will generally repeat steps 1-6 above at least three or more times. 

We’ll work on that stuff later — for now, let’s just focus on mastering the basics!

What happens when you wind up with a little extra left over, you might ask? While it can look pretty scary, it’s simple to solve.

To do this, you’ll repeat steps one through five above until you get a number that cannot continue to be divided evenly. At this point, you’ll do a few additional steps:

• Determine how many times the divisor goes in to the product of your current answer and the divisor. This won’t be a clean number, and that’s OKAY — that’s what your remainder process is for.
• Complete the subtraction steps. After you get your number, complete the subtraction steps and write your answer below the subtraction bar.
• For example: In the case of 16 ➗ 3, we would write the quotient as: 5R1.

When you see that there’s zero left over, or if there is no way for the divisor to divide into the dividend, that means that your problem is solved!

Let’s practice together

• We ask: “How many times can 6 go into 2?” 
• 6 is greater than 2, so we will not be able to put a number over the 2. We then consider, “How many times can 6 go into 20?”
• Well, this is a bit of a challenge! 6 does not go into 20 evenly. 6 x 3= 18, and 6 x 4= 24. So, 6 can go into 20 three times, but it won’t go evenly.
• So, we add the 3 over the 0, above the division bar.
• We put the product of 6 x 3 (our divisor x our quotient) under the dividend and subtract to determine if the a remainder in our difference. 
• There is a remainder of 2. We write our quotient as: 3R2 .

• We know that our divisor is going to be 1, and our dividend (the number being divided) is 5. We identify them, and we put them properly into a division bar. 
• We ask: “How many times can 1 go into 5?” 
• Instead of working the problem counting or using multiplication, we remember the Division By 1 Property. 
• We put 5 at the top of our division bar, since any integer that is divided by 1 will always be itself. 
• There is no remainder for these types of Division By 1 Property problems. We can move on to the next problem.

• We know that our divisor is going to be 2, and our dividend (the number being divided) is 0. We identify them, and we put them properly into a division bar. 
• We ask, “How many times can 2 go into 0?” 
• Instead of working the problem counting or using multiplication, we remember the Division Of 0 By (Any) Number Property. 
• We put 0 at the top of our division bar, since any integer that attempts to divide 0 as a dividend will always result in a quotient of zero. 
• There is no remainder for these types of Division Of 0 By (Any) Number Property problems. We move on to the next problem.

Ready to give it a go?

You’ve done great so far — and you’re well on your way to mastering the art of division. Don’t be afraid to keep trying and make mistakes. 

Practice makes perfect, so we’ve given you a few more problems to practice as you work to perfect your skills. Remember: You can always scroll up to walk through the tutorials and refresh yourself on the terms, placement, and properties you’ll need to solve these correctly. 

By the end of this session, we’re confident that you’ll be ready to claim that A+ on your next math test. You can do it!

Click to reveal the answer.

The answer is 2 .

The answer is 1R6 .

The answer is 4 . 

Parent Guide

The answer is 2.

How did we get here? 

• We identify 4 as the dividend and 2 as the divisor, and place them in the division bar. 
• We ask: “How many times can 2 go into 4?” We determine this using the “count by twos” method, which shows us that 2 goes into 4 a total of two times. 
• We put 2 at the top of our division bar as the quotient, and multiply it by our divisor (2). We then subtract the product of our multiplication from the number to get an answer of 0, which shows us that there is no remainder. You’re done!

The answer is 1R6.

• We identify 8 as our divisor and 14 as our dividend, and place them in the division bar. 
• We ask: “How many times can 8 go into 14?”, as 8 will not go into 1. We determine this using the “count by eights” method, which shows us that 8 goes into 14 just once. 
• We write a 1 in the quotient place above the 4 under the division bar. We then multiply 1 x 8 to get a product of 8, which is placed below the 14 under the division bar. 
• Now, we do the math and subtract 8 from 14. We’ll get 6 as our difference. 
• We then write our quotient as 1R6.

The answer is 4. 

How did we get here?

• We identify 5 as our divisor and 20 as our dividend, and place them in the division bar. 
• We ask: “How many times can 5 go into 20,” as 5 will not go into 2 at all. We determine this using the “count by fives” method, which shows us that 5 can go into 20 cleanly four times. 
• We place a “4” in our quotient place, and multiply 4 x 5 to get a product of 20. This is written under the division bar as a subtraction problem. 
• We subtract 20 – 20, resulting in a difference of 0. 
• This means that 4 is our final quotient with no remainder.

Sign up for the DoodleMath app today!

Turn math into an adventure when you sign up for DoodleMath.

Click here to get started for free!

FAQs about math strategies for kids

We understand that diving into new information can sometimes be overwhelming, and questions often arise. That’s why we’ve meticulously crafted these FAQs, based on real questions from students and parents. We’ve got you covered!

Division is the mathematical process that breaks down a big value into smaller values. 

There are plenty of times you’ll use division in your everyday life. Some of the most common ways might be to break up an even quantity of something, determining how much of an ingredient to use, or grouping up items for use. 

Division is the inverse of multiplication. This means that it naturally undoes any sort of operation that’s done with multiplication. 

The three main parts of division are the divisor, dividend, and quotient. 

Related Posts

Helpful description

Lesson credits

Christina Levandowski

Christina has written for hundreds of clients from small businesses to Indeed.com. She has extensive experience working with marketing strategy and social media marketing, and has her own business creating assets for clients in the space. She enjoys being an entrepreneur and has also started pursuing investment opportunities as time permits.

Parents, sign up for a DoodleMath subscription and see your child become a math wizard!

What we offer

Quick links

All rights reserved. 

Are you a parent, teacher or student?

Get started for free!

Maths information pack

We ask for your contact info so we can send our info pack directly to your inbox for your convenience, exam prep information pack, case studies information pack.

Book a chat with our team

I’m new to Doodle

My school is already using Doodle

Information pack

We ask for your contact info so that our education consultants can get in touch with you and let you know a bit more about doodle., student login, which programme would you like to use.

DoodleMaths

DoodleTables

DoodleEnglish

DoodleSpell

If you’d like to use Doodle’s browser version, please visit this page on a desktop.

To log in to Doodle on this device, you can do so through our apps. You can find out how to download them here:

High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

Free ready-to-use math resources

Hundreds of free math resources created by experienced math teachers to save time, build engagement and accelerate growth

Division For Kids: How To Teach 3 Division Methods From Kindergarten To 5th Grade

Sophie Bartlett

We’ve worked with elementary math experts to create a parent’s guide to division, using arrays, area models and the dreaded standard algorithm (long division).

In here we’ve explained everything you need to know to help your child with these tricky topics!

It doesn’t matter whether you are dividing using an array, area model, or the standard algorithm , for many children and their parents just the mere mention of the ‘D’ word can send shivers down the spine of many young mathematicians, but it doesn’t need to be the case!

Here at Third Space Learning we are on a mission to make math accessible for all, and this includes using arrays, area models, and long division too…

In the past, division was taught without much concrete modeling (using physical items to help represent the math problem), so it’s no wonder that many of us parents find it difficult to this very day.

Nowadays though, with children spending a lot of time at school understanding how division works, rather than just memorizing the method, the fear around division is melting away. Recapping and helping your child to do division at home will make a big difference.

But before you find out everything you need to know about division for kids, we’ve prepared a brief division recap for you!

This blog is part of our series of blogs designed for teachers, schools and parents supporting home learning .

Teaching Long Division Worksheets

Download this free long division worksheet to help your students develop their division skills.

What is division in math?

What are rectangular arrays, what is the area model, what is the standard algorithm, terminology you need to know when teaching division, parts of a division problem labeled for kids and parents, what does my child need to know about division methods in elementary, some simple word problems for k – 2nd grade, division and commutativity in 3rd grade, schools following common core, other schools, using arrays in division, using area models in division, using the standard algorithm to divide up to a four digit number by single digit, how to help kids divide a three or four digit number by a single digit number, division with remainders, dividing by a multi-digit divisor, the standard algorithm (long division) for kids explained, how to do long division: an easy step by step long division method, dividing with decimals, an example of dividing with decimals, how do we know when to divide and which method to use, division assessment questions, division methods in a nutshell.

We know how difficult division can be for both you and your child, so let’s start off with some definitions and a recap of what you may have forgotten since school.

Division is the operation that is the opposite of multiplication and it involves splitting into equal parts or groups.

In elementary school, 3 methods of division are taught, each of which vary in difficulty. They are:

• Area Models
• Standard Algorithm (long division)

Rectangular arrays are a visual representation that can be used in both multiplication and division. The array is organized into equal columns and rows. The rows and columns represent the number of groups and the number of objects in each group, or the size of each individual group. 

The area model is a rectangular model that can be used in both multiplication and division. In division, the quotient (answer) and the divisor are used to define the length and width of the rectangular model. 

The standard algorithm, or long division, is a method that is used when dividing a large number (usually three digits or more) by a single- or multi-digit number.

Your child will be introduced to division using pictures and visual representations, arrays and the area model, and will ultimately use the standard algorithm.

Once the standard algorithm is introduced, your child should start with a smaller number as the dividend and a single digit divisor. Once they feel comfortable with the strategies, they can be used to solve a division problem with a very large dividend by following a series of easy steps.

For example:

In this example four goes into nine two times, and it leaves a remainder of one.

This remainder is then passed onto the next number (six) to make it 16. Four goes into 16 four times, so when put together the answer becomes 24.

We have a very detailed article written for teachers on this subject you might enjoy if you want to go into more depth about teaching the long division method .

In our blogs we try to avoid too much jargon, but the following three terms really are essential to know for anyone looking at division.

• The dividend is the number you are dividing’.
• The divisor is the number you are dividing by.
• The quotient is the amount each divisor receives i.e. the answer in most cases.

A good way to remember it is dividend ÷ divisor = quotient

By learning the correct vocabulary of all the parts of a division problem, your child will find lots of elements of division much simpler.

With division for kids changing from year to year throughout elementary school, there is a lot to cover in the blog, but to help you out we’ve broken it down on a year by year basis.

Division in Primary Grades (K-2): how you can help

In the US, students are not introduced to the term “division” until 3rd grade. This doesn’t mean that you cannot start helping your child build some foundations that would help them when they begin division.

Division is usually referred to as sharing in the lower grades and is introduced using concrete items like counters, blocks, or even items of food such as pasta. This helps children to understand division as sharing between groups.

A simple example of this can be found below.

Grab a set of blocks and help your child try to figure out these sample problems.

Make sure that you remember to use words like share, divide, and equal groups throughout so that your child becomes familiar with the concepts. As your child moves up in grade level, you can increase the number of blocks they begin with, with 40 being maximum in 2nd grade.

Start with 4 blocks. Share them into 2 equal groups.

Start with 10 blocks. Share them into 2 equal groups.

Start with 6 blocks. Share them into 3 equal groups.

Division for 3rd grade: how you can help

In 3rd grade, your child will be formally introduced to division. Your child will need to be able to divide within 100 using different strategies. These strategies include arrays, area models, and strip diagrams. 

Before jumping into division strategies, a key concept to understand and really get to grips with at this age is commutativity .

If you are struggling to remember exactly what commutativity means, the definition is simple.

In math, the commutative property states that order does not matter.

Multiplication is commutative; you can switch around the numbers and it makes no difference.

Division is not commutative. If you switch the order of the numbers, it changes the answer.

2 ÷ 4 = 0.5

At this age, it’s good to master the 2, 5, and 10 multiplication tables with their corresponding division facts. For example:

Multiplication fact:

Corresponding division facts:

Knowing these facts makes division much easier later on, and they are a great example of why commutativity is important.

If your child is comfortable with the difference between 10 ÷ 5 and 10 ÷ 2 even after seeing that 5 x 2 is the same as 2 x 5, they will be best placed to move comfortably up to higher elementary grade division.

Your child will be focusing on writing down division calculations and solving simple division problems that involve missing numbers.

This missing number problem will help you see why multiplication knowledge makes division much easier:

20 ÷ __ = 5

There are two visual methods that are introduced at this age, arrays and area models, and they are broken down below.

Division for Upper Elementary (3rd – 5th grade)

Starting in third grade, students will begin dividing up to 100, using equal groups, arrays and drawings. In 4th grade, your child will be expected to use arrays and/or area models to calculate four-digit dividends and one-digit divisors. Moving into 5th grade, your child will calculate whole number quotients with four-digit dividends and two-digit divisors. It is typical to begin using the standard algorithm, or long division, in 5th grade. 

Based on your child’s state and school curriculum, they may be introduced to different strategies in different grade levels. The strategies are explained below.

Division methods for kids

Unlike how you and I began our division journey, your child will most likely be introduced to division by using pictures. This is the next step in the progression past using concrete objects, as they did in the primary grades. 

In this strategy, students will be provided a graphic that will represent the division equation they are to solve. Because your child can see the graphic, they are able to use it to group the objects, by circling or crossing out, to represent one group.  See the graphic below for an example:

The area model is a rectangular model that uses the length and width to help students visualize division. It is more abstract than arrays, and should be used after your child has a good grasp on simple division concepts. 

The rectangular model represents the total area that the shape takes up. When using this model for multiplication, you would multiply the length by the width to find the area. However, when using the area model for division, you are given the total area (dividend), and the width (divisor), and you will need to calculate the length (quotient). 

The standard algorithm, or long division, at the beginning involves single digit divisors and 3 or 4 digit dividends.

Sit down with your child and take a look at the diagram below to get to know the names and places for each part of the division problem.

They can look very unfamiliar when you’re used to writing your sums out in a line, so work with your child to ensure they know their divisor from their dividend!

By this stage the process of dividing becomes much more of a struggle if your child doesn’t have their multiplication tables by heart so one of the best things you can do for them is support the learning of these.

Here’s a graphic detailing how to divide a three or four digit number by a single digit number.

Remainders can be a tricky concept to grasp when children are first introduced to long division, but it is important that your child understands them well as they can drastically change depending on the question that is being asked.

They’ll also need to choose what kind of remainder to use depending on the question, and some common questions will involve real-life situations, like sharing groups between cars or items between boxes.

The key when it comes to the standard algorithm for kids is to go slow and encourage them to present their work neatly so that they can spot mistakes easily and work to rectify them.

Even when knowing this though, long division can still be a daunting prospect for children (and parents alike!), so take a look at our example below to get to grips with how to tackle a long division problem.

The example below shows one of the most popular ways to divide. This is most likely the way you were taught in school and are familiar with.  All you’ll need to complete the calculation 528 ÷  24 is a pen, some paper and a child who is willing to practice with this method!

After having a go at a few long division questions (with your help to begin with), your child will soon see that this method can help them figure out how to work out long division problems regardless of the numbers involved

Don’t worry if it takes a while to truly embed the process. It’s a long chain of things to remember, so it’ll take regular practice to get this method memorized.

Just remember the process: divide, multiply, subtract, bring down; and repeat.

Hard work will pay off in the long run, so it is worth putting the time in with your child now to make sure long division is explained well early on to lessen the number of times you will hear the inevitable:

“Mommmmm…….How do you do long division…?”

The standard algorithm will be used for numbers involving decimals for the first time in upper elementary.

This means that it is a good time to revise place value so that your child understands how decimals work.

Decimals are parts of a whole (similar to fractions), but the important thing to remember when it comes to dividing decimals is that place value columns decrease in value each time you move to the right.

Different division questions call for different methods of division to solve them, but here is a quick and easy guide to show which method your child should use and when:

• Arrays are best for smaller numbers and arithmetic.
• Area models are great for dividing larger numbers by one digit numbers.
• Long division is handy for dividing large numbers by numbers with 2 or more digits.

Of course there may be occasions when each of the above methods can be used in slightly different scenarios, but as a general rule this should be enough to help your child make the right decision.

When it comes time to take math assessments it is more than likely that your child will have to answer some division based questions.

Problem solving and reasoning can be tricky when it comes to division problems. Often, the problems require more than one operation to be solved which can add an element of complication into an already stressful environment, so encourage your child to look out for words like share or group to help them identify what needs to be done to solve the problem.

It’s easy to spot these questions because they will use the division symbols, either:

or they may involve fractions.

As a rule of thumb, encourage your child to divide mentally where possible.

While written methods are great for bigger numbers, being able to divide mentally will give them an edge. It means that when they are done using the written method, they will be able to see whether or not their answer is roughly correct by estimating.

That should have covered everything you need to know about division for kids. If you’re looking for more ways to help with math homework, then we recommend you also take a look at the following ‘parent and child explainer’ guides too.

• Fractions for Kids: How to Help at Home
• How To Learn Multiplication at Home
• Word Problems Explained with Examples
• Divisibility Rules

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.

Related articles

25 Addition Word Problems For Grades 1-5 With Tips On Supporting Students’ Progress

What Is Box Method Multiplication? Explained For Elementary School Teachers, Parents And Pupils

20 Word Problems For 2nd Grade: Develop Their Problem Solving Skills Across Single and Mixed Topics

20 Multiplication Word Problems for 3rd to 5th Grades With Tips On Supporting Students’ Progress

Math Intervention Pack Operations and Algebraic Thinking [FREE]

Take a sneak peek behind our online tutoring with 6 intervention lessons designed by math experts while supporting your students with Operations and Algebraic Thinking.

As with our full library of lessons, each one includes questions to ask, ways to support students when they are stuck, and answers to the given questions.

Privacy Overview

Long Division

Below is the process written out in full. You will often see other versions, which are generally just a shortened version of the process below . You can also see this done in Long Division Animation .

Let's see how it is done with:

• the number to be divided into is called the dividend
• The number which divides the other number is called the divisor

And here we go:

To divide means to separate into parts. Given the problem 12 ÷ 6, which is read as "twelve divided by six," we can think of division as "how many groups of 6 can we separate 12 into?" The solution, also referred to as the quotient , is 2. Similarly, 12 ÷ 2 = 6, meaning that 12 can be separated into 6 groups of 2. Below is a figure showing these two division problems using objects.

To learn how to perform long division, refer to the long division page. Long division is an algorithm that can be used to systematically divide any number, including larger numbers as well as numbers that involve decimal places.

Division symbols

There are a number of ways to express division using different symbols. The following are all examples of the same division problem:

The first two simply use different division symbols, "÷" and "/". The third is a fraction, or a ratio, that can also be looked at as a division problem, and the last is the format used for long division.

• Get started with computers
• Learn Microsoft Office
• Apply for a job
• Improve my work skills
• Design nice-looking docs
• Getting Started
• Smartphones & Tablets
• Typing Tutorial
• Online Learning
• Basic Internet Skills
• Online Safety
• Social Media
• Zoom Basics
• Google Docs
• Google Sheets
• Career Planning
• Resume Writing
• Cover Letters
• Job Search and Networking
• Business Communication
• Entrepreneurship 101
• Careers without College
• Job Hunt for Today
• 3D Printing
• Freelancing 101
• Personal Finance
• Sharing Economy
• Decision-Making
• Graphic Design
• Photography
• Image Editing
• Learning WordPress
• Language Learning
• Critical Thinking
• For Educators
• Translations
• Staff Picks
• English expand_more expand_less

Multiplication and Division  - Long Division

Multiplication and division  -, long division, multiplication and division long division.

Multiplication and Division: Long Division

Lesson 5: long division.

/en/multiplicationdivision/introduction-to-division/content/

Long division

When you divide a number, you are splitting it equally . In Introduction to Division , you learned that division can be a way to understand real-life situations. For example, imagine a car dealership has 15 cars. The manager wants the cars parked in three equal rows.

You could write the situation like this and use a times table to solve it:

After the cars are divided, counting them shows that each row should have five cars. Now, let's say the car dealership has 42 cars and the manager wants to park them in three rows. The situation would look like this:

This problem is harder to solve. It would take a lot of time to divide that many cars into three groups. Plus, there's no 42 in the 3's column on the times table. Fortunately, there is a way to set up the problem that makes it easy to solve one step at a time. It's called long division .

Let's learn how to set up these problems. We'll look at the problem we discussed above: 42 / 3 .

In the last lesson, we learned how to write division expressions.

However, dividing a larger number is easier when the expression is written in a different way.

Instead of writing the numbers side by side with a division symbol...

Instead of writing the numbers side by side with a division symbol... we'll use a different symbol called a division bracket .

The number you're dividing goes under the division bracket. That's 42 .

To the left of the division bracket, write the number you're dividing by. In our problem, it's 3 .

The division bracket is also an equals sign. The quotient , or answer, is written above it.

Let's try setting up another expression, 125 / 5 . First, write the division bracket.

Next, write the number being divided, 125 .

Finally, write the number we're dividing by, 5 .

Remember, you should be careful to set up long division problems correctly.

The number you're dividing goes under the division bracket...

The number you're dividing goes under the division bracket... and the number you're dividing by goes to the left of it.

Solving long-division problems

To solve long division problems, you'll use three math skills you've already learned: division , multiplication , and subtraction . It's a good idea to make sure you feel comfortable with all three skills. If you think you might need more practice, take some time to review those lessons first.

When solving a long division problem, the number under the division bracket is split into smaller numbers. This makes division easier. Plus, you can use a familiar tool, like a times table, to help.

Let's see how solving a long division problem works.

Remember the manager of the used car dealership who wanted to divide 42 cars among 3 rows? Let's find out how many cars he should put in each row.

We'll use long division to solve this problem: 42 / 3 .

Long division follows a pattern . You follow the same basic steps again and again until the problem is complete. If this seems confusing, don't worry. We'll go through it step by step.

We'll begin with the left digit under the division bracket. That means we'll start with the 4 ...

We'll begin with the left digit under the division bracket. That means we'll start with the 4 ... and we'll figure out how many times it can be divided by 3 .

Now it's time to solve 4 / 3 .

We can use the times table . We'll look at the 3's column.

Since 4 is the number we're dividing, we need to locate the number that is the closest to 4. The number can't be any larger than 4 .

3 is the closest to 4 .

Next, we'll find the row 3 is located in. It's the 1's row.

That means 3 goes into 4 one time.

We'll write 1 above the 4 and the division bracket.

The next step is to multiply the 1 and 3 .

Whenever you multiply a number by 1, that number stays the same. So 1 x 3 is 3 .

We'll write 3 below the 4 .

The next step is to subtract .

Now we solve 4 - 3 .

4 - 3 is 1 . We'll write 1 below the 4 and 3 .

Since our answer is 1 , we're not done yet. We'll know our problem is complete when the answer to our subtraction problem is zero. Plus, there's still another digit under the bracket: 2 .

We'll bring the 2 down and rewrite it next to the 1 .

See how the 1 and 2 look like the number 12 ? That's the next number we need to divide.

12 is large enough to be divided, so we'll figure out how many times it can be divided by 3 .

Let's look at the 3's column. Since 12 is the number we're dividing, we'll find the number closest to 12 . Remember, the number can't be any larger than 12 .

The 3's column has a 12 . It would be impossible to get closer than that!

Now we find the row 12 is located in.

It's the 4's row. 3 goes into 12 four times.

We'll write 4 above the 2 and the division bracket.

Now it's time to multiply the 4 and 3 .

4 x 3 is 12 .

Write the 12 beneath the 12 .

We'll set up our subtraction problem.

Now it's time to solve 12 - 12 .

12 - 12 is 0 . Write 0 beneath the line directly below the 2 and 2 .

The answer to our subtraction problem is 0 . That means we're done! 42 / 3 = 14 .

Solve these long division problems. Then, check your answer by typing it in the box.

Problems with remainders

In Introduction to Division , you learned that some numbers can't be equally divided. When that happens, there will be an amount left over. This is called a remainder . For instance, let's say you want to share 8 treats equally among your 3 dogs. The answer is that each dog would get two treats with a remainder of two .

The remainder is written as part of the quotient: 8 / 3 = 2 r2 .

Long division problems can have remainders too. Watch the slideshow to see how.

Let's try this problem, 49 / 4 .

As always, start by dividing the left digit. This means we'll solve for 4 / 4 .

4 / 4 is 1 .

Next, we'll multiply the answer we just got, 1 , by the number we're dividing by, 4 . So 4 x 1 .

4 x 1 is 4 .

Next, subtract 4 - 4 . Whenever you subtract a number from the same number, the answer is 0 . So 4 - 4 = 0 .

Our problem's not done. The next digit in the number we're dividing is 9 . We'll solve for 9 / 4 .

9 / 4 is 2.

Again, we'll multiply the number we just wrote by the number we're dividing by.

2 x 4 is 8 .

We'll subtract that number, 8 , from the number we were dividing.

9 - 8 is 1 .

Since 1 is smaller than 4, we can't divide it any further. 1 is our remainder . We'll write it next to the rest of the answer.

We're done! 49 / 4 = 12 , with a remainder of 1 .

Solve these division problems with remainders. Then, check your answer by typing it into the boxes.

Decimal quotients

On the last page, you learned how to find the remainder for a long division problem that can't be solved evenly. Remainders can be useful if you need to know how much is left over when you divide something, but they might not be very useful in every situation. For example, what if you wanted to divide a 9- foot-long board into 4 equal pieces ? That problem could look like this:

9 / 4 = 2 r1

In other words, when you divide a board that's nine feet long into four pieces , each piece will be two feet long . There will be one foot left over.

What if you don't want to waste any wood? In that case, you can continue to divide until there is no longer a remainder. That way, you'd have four equal pieces of wood, with none left over. That problem would look like this:

9 / 4 = 2.25

The answer, 2.25, is a decimal number. You can tell, because it includes a symbol called a decimal point (.) . The number to the left of the decimal point , 2 , is the whole number. The rest of the answer, .25 , shows the part of the number that didn't divide evenly.

Click through the slideshow below to learn how to find the decimal answer to a division problem.

Let's say we have 62 treats to divide equally among 4 dogs. The problem we're solving is 62 / 4 . Let's find out how many treats each dog should get.

As always, we'll begin with the left digit under the division bracket. That means we'll start with the 6 ...

As always, we'll begin with the left digit under the division bracket. That means we'll start with the 6 ... and we'll figure out how many times it can be divided by 4 .

Now it's time to solve 6 / 4 . We'll use the times table.

We'll look at the 4's column. Since 6 is the number we are dividing, we need to find the number that is closest to 6 . Remember, it can't be any larger than 6 .

4 is the closest to 6 .

Next, we'll find the row 4 is located in. It's the 1's row.

That means 4 goes into 6 one time. We'll write 1 above the 6 .

Next, we'll multiply the 1 and 4 .

Remember, whenever you multiply a number by 1, that number always stays the same. So 1 x 4 is 4 .

We'll write 4 below the 6 .

The next step is to subtract.

Now we solve 6 - 4 .

6 - 4 is 2 . We'll write 2 below the line.

Since 2 is more than zero, we know we're not done with our problem.

We'll bring the 2 down and rewrite it next to the 2 .

22 is large enough to be divided, so we'll figure out how many times it can be divided by 4 .

Let's look at the 4's column to locate the number closest to 22 . The number can't be any larger than 22 .

20 is the closest to 22 .

Now we'll find the row 20 is located in. It's the 5's row. So 4 goes into 20 five times.

We'll write 5 above the 2 .

Now we need to multiply the 5 and 4 .

5 x 4 is 20 .

We'll write 20 beneath the 22 .

Now it's time to solve 22 - 20 .

22 - 20 is 2 . We'll write 2 beneath the line directly below the 2 and 0 .

The answer to the last subtraction problem is more than zero, so we'll look under the bracket to see if there is another digit we can bring down.

We've divided both of those digits. That means there are no more digits to bring down. But if we write another digit next to 62 , we could bring that digit down.

We don't want to make the 62 any larger. That would change our problem. We only had 62 bones to divide.

So next to the 62 , we'll write the number that means nothing: 0 .

But that changes 62 into a larger number: 620 . That won't work.

So to keep the value of 62 this same, we'll add a decimal point between the 62 and the 0 .

This means our quotient needs a decimal as well. So we'll write a decimal point next to the 15 directly above the other decimal.

Now we can continue to solve the problem. We'll bring the 0 down and rewrite it next to the 2 .

Let's figure out how many times 20 can be divided by 4 .

Look at the 4's column. 20 is the number we are dividing, so we'll find the number that is the closest to 20 but not larger than 20 .

The 4's column has a 20 . That's as close as we can get!

Now we find the row 20 is located in. It's the 5's row. 4 goes into 20 five times.

We'll write 5 above the 0 .

Now it's time to multiply the 5 and 4 .

Write 20 beneath the 20 .

Time to solve 20 - 20 .

20 - 20 = 0 . Write 0 below the line directly below the 0 and 0 .

The answer to the subtraction problem is 0 . That means we have completed the problem. So 62 / 4 = 15.5 .

Sometimes, you may notice that a decimal can start to repeat as you continue to add zeros under the division bracket. This is known as a repeating decimal. When this happens, you can place a horizontal line over the digit that repeats.

Look at the image below. A horizontal line has been placed over the repeating digit.

Another way to handle a repeating decimal is to round it. Rounding creates a new number that has a value close to the original number.

When rounding a repeating decimal, you'll reduce the number of digits that come after the decimal point. First, decide which digit you are rounding to. Then look at the digit to the right of it. If the digit is 5 or more, increase the rounded digit by 1. If it is 4 or less, the rounded digit stays the same. The other digits after the rounded digit are not written.

Look at the image below. In this case, each of these repeating decimals has been rounded to the second digit after the decimal point.

Find the decimal quotient for each of the long division problems below.

Checking your work

Checking your work after you divide is a good habit to develop. Checking helps you know that your answer is correct. To check the answer to a division problem, you'll need to use multiplication.

Let's look at this problem: 54 / 6 = 9 .

How do we know that 9 is the correct answer? We can check by multiplying.

Let's set up our multiplication problem. First, we'll write the quotient. That means we'll write 9 .

Next, we'll multiply the number that we divided by, 6 .

Time to multiply. 9 x 6 = 54 .

If we divided correctly, the answer will match the larger number in the division problem.

They are both 54 . We checked the problem, and it was correct!

Let's try checking another problem. This time, the quotient has a remainder: 20 / 3 = 6 r2 .

Let's set up our multiplication problem. First write the quotient without the remainder. That's 6 .

Then multiply the amount that the larger number was divided by, 3 .

Now it's time to multiply. 6 x 3 = 18 .

Let's check to see if our answer matches the larger number in the division problem — 18 and 20 . No, they aren't equal.

That may be because we haven't included the remainder, 2 .

Since the answer to the division problem has a remainder...

Since the answer to the division problem has a remainder... just multiplying should give you a number less than the original number.

We'll set up an addition problem to add the 2 to 18 .

Now add 18 and 2 .

18 + 2 is 20 .

Finally, check to see if 20 matches the larger number in the division problem. It does!

In the slideshow, we used multiplication to check our division. The answer to the multiplication problem should always be the same as the larger number in the division problem. If your two answers don't match, check to see if you added the remainder. If your answers are still different, you might have made a mistake the first time you were dividing. Try solving the problem again.

Long division with decimals

In this lesson, you also learned how to solve division problems that have a decimal in the answer. Checking your work for this type of problem is similar to checking other division problems. You'll follow the same steps.

We'll try checking this problem: 57 / 5 = 11.4 .

Let's set up our multiplication problem.

We'll write the decimal quotient, 11.4 .

Next, we'll multiply the number that we divided by, 5 .

Now it's time to multiply: 11.4 x 5 .

Since the quotient had one digit to the right of the decimal point...

Since the quotient had one digit to the right of the decimal point... we write the answer with one digit to the right of the decimal point. 11.4 x 5 = 57.0 .

Finally, we'll check to see if 57.0 matches the larger number in our division problem. They are the same. Our answer was correct.

Practice division by solving these problems. There are 3 sets of problems. Each set has 5 problems.

Set 2: Type your answer using remainders.

Set 3: type your answer using decimals..

/en/multiplicationdivision/video-division/content/

Long Division Alternative: The Area or Box Method

• By Shelley Gray
• January 11, 2018

Long division is often considered one of the most challenging topics to teach. Luckily, there are strategies that we can teach to make multi-digit division easier to understand and perform.

The Box Method , also referred to as the Area Model , is one of these strategies. It is a mental math based approach that will enhance number sense understanding. Students solve the equation by subtracting multiples until they get down to 0, or as close to 0 as possible.

If you plan on teaching the partial quotients strategy in your classroom (which I highly recommend) the Box Method is a great way to get started. It uses the same steps as partial quotients , but is organized a bit differently.

Let’s learn how to perform the Box Method/Area Model for long division!

Wait! Are you looking for the Area Model for multiplication rather than division? Find it HERE.

Below, I have included both a video tutorial and step-by-step instructions.

VIDEO TUTORIAL

AREA MODEL/BOX METHOD FOR LONG DIVISION: STEP-BY-STEP INSTRUCTIONS 

Suppose that we want to solve the equation 324÷2.

Step 1: First we draw a box. We write the dividend inside the box, and the divisor on the left side.

Step 2: We want to figure out how many groups of 2 can be made from 324. We will do this in parts to make it easier. We could start by making 100 groups of 2, since we know that we have at least this many groups. So we multiply 100×2 to make 200, and then take that 200 away from 324. Now we have 124 left.

Step 3: We make another box and carry the 124 over to it. Now let’s take away another easy multiply of 2. How about 50 groups of 2? We know that we can take out another 50 groups of 2 from 124. 50×2=100, so we take 100 from 124. Now we have 24 left.

Step 4: We make another box and carry the 24 over to it. We know that 12 groups of 2 makes 24, so let’s write a 12 on top and take away 24 from the 24. Now we end up with 0, so we know that we are finished our equation.

Step 5: Now we add the “parts” from the top of the boxes to find our quotient. 100+50+12=162, so we know that 324÷2=162.

ONE MORE EXAMPLE (WITH A REMAINDER)

Let’s take a look at one more example. In this example, we will solve 453÷4.

• First we wrote our dividend inside the box, and our divisor on the left side.
• We took out 100 groups of 4 first. This made 400. We subtracted 400 from 453 and were left with 53.
• We carried the 53 to the next box, and then took out another 10 groups of 4 to make 40. We took the 40 away from the 53 and were left with 13.
• We carried the 13 over to the next box, and then took out 3 groups of 4 to make 12. We took the 12 away from the 13 and were left with 1.
• We cannot take any more groups of 4 out, so our remainder is 1. To find our final quotient, we add 100+10+3+remainder 1 to make 113 R1.

The Area Model for Multiplication

The area model is fantastic for multiplication as well! If you’d like to read about how to teach this in a concrete way, here’s a post you may be interested in.

BOX STRATEGY/AREA MODEL TASK CARDS

These task cards give students the opportunity to practice the box method/area model for long division in a variety of different ways. Students will calculate quotients, solve division problems, figure out missing dividends and divisors, think about how to efficiently solve an equation using the box method, and more. See the Box Method Task Cards HERE or the Big Bundle of Long Division Task Cards HERE .

THE LONG DIVISION STATION

The Long Division Station is a self-paced, student-centered math station for long division. Students gradually learn a variety of strategies for long division, the box method being one of them. One of the greatest advantages to this Math Station is that is allows you to target every student and their unique abilities so that everyone is appropriately challenged. See The Long Division Station HERE.

OR SEE ALL RESOURCES

Pingback: Partial Quotients: an alternative for traditional long division - Shelley Gray

Pingback: The Grid Method for Long Division - Shelley Gray

Pingback: Effective Alternatives for Long Division - Shelley Gray

Very well taught, understandable. Thanks. Substitute gets it.

That is wonderful! My son uses the box method for multiplication , but becomes visually frustrated and angry when he was figuring out long division today. I have never seen this method before in my life. Totally makes sense. Thank you

love it so easy to work with

Pingback: Primary, Junior Maths – Qaawyrdprimary

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed .

Free Fast Finisher Activities

Master the Multiplication Facts!

Make math relevant!

A fun math game!

The Best Way to Teach Multiplication Facts

COPYRIGHT © 2018 — SHELLEY GRAY • ALL RIGHTS RESERVED. SITE BY LAINE SUTHERLAND DESIGNS

Long Division

Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence. Just like the regular division problems, the dividend is divided by the divisor which gives a result known as the quotient, and sometimes it gives a remainder too. Let us learn how to divide using the long division method , along with long division examples with answers, which include the long division steps in this article.

What is Long Division Method?

Long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division . Observe the following long division method to see how to divide step by step and check the divisor, the dividend, the quotient, and the remainder.

The above example also showed us how to do 2 digit by 1 digit division.

Parts of Long Division

While performing long division, we need to know the important parts of long division. The basic parts of long division can be listed as follows:

The following table describes the parts of long division with reference to the example shown above.

How to do Long Division?

Division is one of the four basic mathematical operations, the other three being addition , subtraction , and multiplication . In arithmetic, long division is a standard division algorithm for dividing large numbers, breaking down a division problem into a series of easier steps. Let us learn about the steps that are followed in long division.

Long Division Steps

In order to perform division, we need to understand a few steps. The divisor is separated from the dividend by a right parenthesis 〈)〉 or vertical bar 〈|〉 and the dividend is separated from the quotient by a vinculum (an overbar). Now, let us follow the long division steps given below to understand the process.

• Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.
• Step 2: Then divide it by the divisor and write the answer on top as the quotient.
• Step 3: Subtract the result from the digit and write the difference below.
• Step 4: Bring down the next digit of the dividend (if present).
• Step 5: Repeat the same process.

Let us have a look at the examples given below for a better understanding of the concept. While performing long division, we may come across problems when there is no remainder, while some questions have remainders. So, first, let us learn division in which we get remainders.

Division with Remainders

Case 1: When the first digit of the dividend is equal to or greater than the divisor.

Example: Divide 435 ÷ 4

Solution: The steps of this long division are given below:

• Step 1: Here, the first digit of the dividend is 4 and it is equal to the divisor. So, 4 ÷ 4 = 1. So, 1 is written on top as the first digit of the quotient.
• Step 2: Subtract 4 - 4 = 0. Bring the second digit of the dividend down and place it beside 0.
• Step 3: Now, 3 < 4. Hence, we write 0 as the quotient and bring down the next digit of the dividend and place it beside 3.
• Step 4: So, we have 35 as the new dividend. We can see that 35 > 4 but 35 is not divisible by 4, so we look for the number just less than 35 in the table of 4 . We know that 4 × 8 = 32 which is less than 35 so, we go for it.
• Step 5: Write 8 in the quotient. Subtract: 35 - 32 = 3.
• Step 6: Now, 3 < 4. Thus, 3 is the remainder and 108 is the quotient.

Case 2: When the first digit of the dividend is less than the divisor.

Example: Divide 735 ÷ 9

Solution: Let us divide this using the following steps.

• Step 1: Since the first digit of the dividend is less than the divisor, put zero as the quotient and bring down the next digit of the dividend. Now consider the first 2 digits to proceed with the division.
• Step 2: 73 is not divisible by 9 but we know that 9 × 8 = 72 so, we go for it.
• Step 3: Write 8 in the quotient and subtract 73 - 72 = 1.
• Step 4: Bring down 5. The number to be considered now is 15.
• Step 5: Since 15 is not divisible by 9 but we know that 9 × 1 = 9, so, we take 9.
• Step 6: Subtract: 15 - 9 = 6. Write 1 in the quotient.
• Step 7: Now, 6 < 9. Thus, remainder = 6 and quotient = 81.

Case 3: This is a case of long division without a remainder.

Division without Remainder

Example: Divide 900 ÷ 5

Solution: Let us see how to divide step by step.

• Step 1: We will consider the first digit of the dividend and divide it by 5. Here it will be 9 ÷ 5.
• Step 2: Now, 9 is not divisible by 5 but 5 × 1 = 5, so, write 1 as the first digit in the quotient.
• Step 3: Write 5 below 9 and subtract 9 - 5 = 4.
• Step 4: Since 4 < 5, we will bring down 0 from the dividend to make it 40.
• Step 5: 40 is divisible by 5 and we know that 5 × 8 = 40, so, write 8 in the quotient.
• Step 6: Write 40 below 40 and subtract 40 - 40 = 0.
• Step 7: Bring down the next 0 from the dividend. Since 5 × 0 = 0, we write 0 as the remaining quotient.
• Step 9: Therefore, the quotient = 180 and there is no remainder left after the division, that is, remainder = 0.

Long division problems also include problems related to long division by a 2 digit number, long division polynomials and long division with decimals. Let us get an an idea about these in the following sections.

Long Division by a 2 Digit Number

Long division by a 2 digit number means dividing a number by a 2-digit number . For long division by a 2 digit number , we consider both the digits of the divisor and check for the divisibility of the first two digits of the dividend.

For example, if we need to divide 7248 by 24, we can do it using the long division steps. Let us see how to divide step by step.

• Step 1: Since it is a long division by a 2 digit number, we will check for the divisibility of the first two digits of the dividend. The first 2 digits of the dividend are 72 and it is greater than the divisor, so, we will proceed with the division.
• Step 2: Using the multiplication table of 24, we know that 24 × 3 = 72. So we write 3 in the quotient and 72 below the dividend to subtract these. Subtract 72 - 72 = 0.
• Step 3: Bring down the next number from the dividend, that is, 4. The number to be considered now is 4.
• Step 4: Since 4 is smaller than 24, we will put 0 as the next quotient, since 24 × 0 = 0 and write 0 below 4 to subtract 4 - 0 = 4
• Step 5: Bring down the next number from the dividend, that is, 8 and place it next to this 4. The number to be considered now is 48.
• Step 6: Using the multiplication table of 24, we know that 24 × 2 = 48. So we write 2 in the quotient and 48 below the dividend to subtract these. Subtract 48 - 48 = 0. Thus, remainder = 0 and quotient = 302. This means, 7248 ÷ 24 = 302.
• Long Division of Polynomials

When there are no common factors between the numerator and the denominator , or if you can't find the factors, you can use the long division process to simplify the expression. For more details about long division polynomials, visit the Dividing Polynomials page.

Long Division with Decimals

Long division with decimals can be easily done just like the normal division. We just need to keep in mind the decimals and keep copying them as they come. For more details about long division with decimals, visit the Dividing Decimals page.

How to Divide Decimals by Whole Numbers?

When we need to divide decimals by whole numbers, we follow the same procedure of long division and place the decimal in the quotient whenever it comes. Let us understand this with the help of an example.

Example: Divide 36.9 ÷ 3

• Step 1: Here, the first digit of the dividend is 3 and it is equal to the divisor. So, 3 ÷ 3 = 1. So, 1 is written on top as the first digit of the quotient and we write the product 3 below the dividend 3.
• Step 2: Subtract 3 - 3 = 0. Bring the second digit of the dividend down and place it beside 0, that is, 6
• Step 3: Using the multiplication table of 3, we know that 3 × 2 = 6. So we write 2 in the quotient and 6 below the dividend to subtract these. Subtract 6 - 6 = 0.
• Step 4 : Now comes the decimal point in the dividend. So, place a decimal in the quotient after 12 and continue with the normal division.
• Step 5: Bring down the next number from the dividend, that is, 9. The number to be considered now is 9.
• Step 6: Using the multiplication table of 3, we know that 3 × 3 = 9. So we write 3 in the quotient and 9 below the dividend to subtract these. Subtract 9 - 9 = 0. Thus, remainder = 0 and quotient = 12.3. This means, 36.9 ÷ 3 = 12.3

Long Division Tips and Tricks:

Given below are a few important tips and tricks that would help you while working with long division:

• The remainder is always smaller than the divisor.
• For division, the divisor cannot be 0.
• The division is repeated subtraction, so we can check our quotient by repeated subtractions as well.
• We can verify the quotient and the remainder of the division using the division formula : Dividend = (Divisor × Quotient) + Remainder.
• If the remainder is 0, then we can check our quotient by multiplying it with the divisor. If the product is equal to the dividend, then the quotient is correct.

☛ Related Articles

• Long Division Formula
• Long Division with Remainders Worksheets
• Long Division Without Remainders Worksheets
• Long Division with 2-digit Divisors Worksheets
• Long Division Calculator

Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12 . Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.

Long Division Examples with Answers

Example 1: Ron planted 75 trees equally in 3 rows. Use long division to find out how many trees did he plant in each row?

The total number of trees planted by Ron = 75. The number of rows = 3. To find the number of trees in each row, we need to divide 75 by 3 because there is an equal number of trees in each of the three rows. Let us also observe how to do 2 digit by 1 digit division here.

Therefore, the number of trees in each row = 25 trees.

Example 2: $4000 needs to be distributed among 25 men for the work completed by them at a construction site. Calculate the amount given to each man.

The total amount is $4000. The number of men at work = 25. We need to calculate the amount given to each man. To do so, we have to divide 4000 by 25 using the long division method. Let us see how to work with long division by a 2 digit number and also see how to do long division step by step.

Each man will be given $160. Therefore, $160 is the amount given to each man.

Example 3: State true or false with respect to long division.

a.) In the case of long division of numbers, the remainder is always smaller than the divisor.

b.) We can verify the quotient and the remainder of the division using the division formula: Dividend = (Divisor × Quotient) + Remainder.

a.) True, in the case of long division of numbers, the remainder is always smaller than the divisor.

b.) True, we can verify the quotient and the remainder of the division using the division formula: Dividend = (Divisor × Quotient) + Remainder.

go to slide go to slide go to slide

Book a Free Trial Class

Practice Questions on Long Division

go to slide go to slide

FAQs on Long Division

What is long division in math.

Long division is a process to divide large numbers in a convenient way. The number which is divided into smaller groups is known as a dividend, the number by which we divide it is called the divisor, the value received after doing the division is the quotient, and the number left after the division is called the remainder.

The following steps explain the process of long division. This procedure is explained with examples above on this page.

• Write the dividend and the divisor in their respective positions.
• Take the first digit of the dividend from the left.
• If this digit is greater than or equal to the divisor, then divide it by the divisor and write the answer on top as the quotient.
• Write the product below the dividend and subtract the result from the dividend to get the difference. If this difference is less than the divisor, and there are no numbers left in the dividend, then this is considered to be the remainder and the division is done. However, if there are more digits in the dividend to be carried down, we continue with the same process until there are no more digits left in the dividend.

What are the Steps of Long Division?

Given below are the 5 main steps of long division. For example, let us see how we divide 52 by 2.

• Step 1: Consider the first digit of the dividend which is 5 in this example. Here, 5 > 2. We know that 5 is not divisible by 2.
• Step 2: We know that 2 × 2 = 4, so, we write 2 as the quotient.
• Step 3: 5 - 4 = 1 and 1 < 2 (After writing the product 4 below the dividend, we subtract them).
• Step 4: 1 < 2, so we bring down 2 from the dividend and we get 12 as the new dividend now.
• Step 5: Repeat the process till the time you get a remainder less than the divisor. 12 is divisible by 2 as 2 × 6 = 12, so we write 6 in the quotient, and 12 - 12 = 0 (remainder).

Therefore, the quotient is 26 and the remainder is 0.

How to do Long Division with 2 Digits?

For long division with 2 digits, we consider both the digits of the divisor and check for the divisibility of the first two digits of the dividend. If the first 2 digits of the dividend are less than the divisor, then consider the first three digits of the dividend. Proceed with the division in the same way as we divide regular numbers. This procedure is explained with examples above on this page under the heading of 'Long Division by a 2 Digit Number'.

What is the Long Division of Polynomials?

In algebra , the long division of polynomials is an algorithm to divide a polynomial by another polynomial of the same or the lower degree. For example, (4x 2 - 5x - 21) is a polynomial that can be divided by (x - 3) following some defined rules, which will result in 4x + 7 as the quotient.

How to do Long Division with Decimals?

The long division with decimals is performed in the same way as the normal division. This procedure is explained with examples above on this page under the heading of 'How to Divide Decimals by Whole Numbers'? For more details, visit the page about dividing decimals . The basic steps of long division with decimals are given below.

• Write the division in the standard form.
• Start by dividing the whole number part by the divisor.
• Place the decimal point in the quotient above the decimal point of the dividend.
• Bring down the digits on the tenths place, i.e., the digit after the decimal.
• Divide and bring down the other digit in sequence.
• Divide until all the digits of the dividend are over and a number less than the divisor or 0 is obtained in the remainder.

Trending Post : Teaching Fractions with Food

5 Fun Division Word Problems | Practice Multiple Ways of Solving | Free Printable

Division word problems.

Are your children ready to conquer division? These interactive, division problem-solving worksheets will help children solve division word problems in five different ways.

Table of Contents

Division Problems

He has done it numerous times. Sharing a group of toys with his siblings, or even sharing a bag of M&M’s. In those situations, he instinctively knows how to do division problems.

When we hit the division problem in his math book, he wasn’t quite as sure what to do.

I wanted this little man of mine to be able to relate division to what he has done over and over while creating strategies for solving division problems.

These word problems with five steps were what we came up with. These simple division worksheets are perfect for 3rd grade division word problems.

How to Solve Division Word Problems

Step 1: division word problem solving by grouping.

The first step is the way we normally teach children to solve division problems. The students grab the amounts of objects that need to be divided up and then place them in the correct amount of groups. It is very hands-on and a visual way for our children to understand what is happening when we are dividing .

Step 2: Solving Division Word Problems by Repeated Subtraction

To solve a word problem using repeated subtraction, students start with the number being divided up or the dividend. Now they subtract the divisor or the number that tells how many groups are needed from the dividend over and over until they reach zero. The number of times they subtracted is the answer.

Step 3: Division Word Problem Solving with Arrays

Chances are if you taught multiplication in a hands-on way, you taught it using arrays. You can create an array when you place objects, pictures, or numbers in equal columns and equal rows.

With multiplication, you would take a problem like 4 x 5, and make 4 rows with 5 in each column. You would end up with 20 objects, which of course is the answer to the multiplication problem.

Division is a little different. If the problem is 18 ÷ 3, The student creates three rows. They then keep placing one object in each row until they have used 18 objects.

They now have an array that is a 3 by 6. The answer to the division problem is 6.

Want to know how to use arrays to divide when the numbers are larger? Check out this POST !

Step 4: Number Line to Solve Division Word Problems

Number lines have become an important tool in helping children solve problems. The beginning of this video by Ramy Melhem  clearly shows how to divide using a number line, and the little frog hopping is a great visual for our little ones.

Step 5: Create an Equation

The final step is very easy after all the work above. The students simply figure out what number was divided up, and place it in the first box.

They then look at how many groups they created, and that is the number that goes into the second box. Finally, they figure out how many objects were in each group and that is the answer or quotient.

That number goes in the last box.

By throwing in markers and painting with q-tips these sheets were fun for my little man, and I could see his understanding of division grow.

We moved on to these cut-and-paste division assessments, and his thinking was challenged even more. Through all this practice he is on his way to mastering simple division problems, and your kiddos can master it too.

Get This Cut and Paste Division Assessment at my TpT Store .

You’ve Got This

Division Word Problems Printable

These free division math problems will help your students learn how to solve division problems 5 different ways. You can download this printable by clicking on the download button.

Similar Posts

Three Manipultives To Use When Teaching Decomposing Fractions

6 Probability Worksheet Grade 3 | Free Printable

Daily Summer Activities Calendar for Kids | Printable | Free

Multi Digit Multiplication Word Problems | Free Worksheet

11 Free 3 Digit Subtraction with Regrouping Worksheets PDF

5 Free Addition Coloring Worksheets PDF

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Unit 3: Multiplication and division

About this unit.

In this topic, we will multiply and divide whole numbers. The topic starts with 1-digit multiplication and division and goes through multi-digit problems. We will cover regrouping, remainders, and word problems.

Multiplication intro

• Multiplication as equal groups (Opens a modal)
• Intro to multiplication (Opens a modal)
• Basic multiplication (Opens a modal)
• Multiplication with arrays (Opens a modal)
• Worked example: Whole numbers on the number line (Opens a modal)
• More ways to multiply (Opens a modal)
• Ways to represent multiplication (Opens a modal)
• Understand multiplication using groups of objects 7 questions Practice
• Multiply with arrays 7 questions Practice
• Represent multiplication on the number line 4 questions Practice

Multiplication facts

• Multiplication tables for 2-9 (Opens a modal)
• Multiplication tables for 10, 11, 12 (Opens a modal)
• Multiply by 0 or 1 14 questions Practice
• Multiply by 2 7 questions Practice
• Multiply by 3 7 questions Practice
• Multiply by 4 7 questions Practice
• Multiply by 5 7 questions Practice
• Multiply by 6 7 questions Practice
• Multiply by 7 14 questions Practice
• Multiply by 8 14 questions Practice
• Multiply by 9 14 questions Practice
• Basic multiplication 7 questions Practice

Properties of multiplication

• Properties of multiplication (Opens a modal)
• Properties and patterns for multiplication (Opens a modal)
• Associative property of multiplication (Opens a modal)
• Commutative property of multiplication review (Opens a modal)
• Associative property of multiplication review (Opens a modal)
• Distributive property review (Opens a modal)
• Commutative property of multiplication 7 questions Practice
• Associative property of multiplication 7 questions Practice
• Distributive property 4 questions Practice

Multiplying by tens

• Multiplying by multiples of 10 (Opens a modal)
• Multiplying by tens word problem (Opens a modal)
• Multiply by tens 7 questions Practice
• Multiply by tens word problems 4 questions Practice

Multiplication by 10s, 100s, and 1000s

• Multiplying 10s (Opens a modal)
• Multiplying 1-digit numbers by multiples of 10, 100, and 1000 (Opens a modal)
• Multiplying 1-digit numbers by 10, 100, and 1000 (Opens a modal)
• Multiplying 10s 7 questions Practice
• Multiply 1-digit numbers by a multiple of 10, 100, and 1000 7 questions Practice
• Multiply 1-digit numbers by 10, 100, and 1000 7 questions Practice

Multiplication: place value and area models

• Using area model and properties to multiply (Opens a modal)
• Multiplying with distributive property (Opens a modal)
• Multiplying with area model: 6 x 7981 (Opens a modal)
• Multiplying with area model: 78 x 65 (Opens a modal)
• Lattice multiplication (Opens a modal)
• Why lattice multiplication works (Opens a modal)
• Multiply 2-digits by 1-digit with distributive property 4 questions Practice
• Multiply 2-digit numbers with area models 4 questions Practice

Multi-digit multiplication

• Multiplying 2-digit by 1-digit (Opens a modal)
• Multiplying 3-digit by 1-digit (Opens a modal)
• Multiplying 3-digit by 1-digit (regrouping) (Opens a modal)
• Multiplying 4-digit by 1-digit (regrouping) (Opens a modal)
• Multiplying 2-digit numbers (Opens a modal)
• Multiplying 2-digit by 2-digit: 36x23 (Opens a modal)
• Multiplying 2-digit by 2-digit: 23x44 (Opens a modal)
• Multiplying multi-digit numbers (Opens a modal)
• Multiply without regrouping 7 questions Practice
• Multiply with regrouping 7 questions Practice
• Multiply 2-digit numbers 7 questions Practice
• Multi-digit multiplication 4 questions Practice

Relating multiplication and division

• Relating division to multiplication (Opens a modal)
• Multiplication word problem: parking lot (Opens a modal)
• Division word problem: school building (Opens a modal)
• Relate division to multiplication 7 questions Practice
• Relate division to multiplication word problems 4 questions Practice

Division intro

• The idea of division (Opens a modal)
• Intro to division (Opens a modal)
• Ways to represent division (Opens a modal)
• Division with groups of objects 7 questions Practice
• Divide with visuals 7 questions Practice

Division facts

• No videos or articles available in this lesson
• Divide by 1 11 questions Practice
• Divide by 2 10 questions Practice
• Divide by 3 10 questions Practice
• Divide by 4 10 questions Practice
• Divide by 5 10 questions Practice
• Divide by 6 10 questions Practice
• Divide by 7 10 questions Practice
• Divide by 8 10 questions Practice
• Divide by 9 10 questions Practice
• Divide by 10 10 questions Practice
• Basic division 7 questions Practice

Division problems that work out nicely

• Quotients that are multiples of 10 (Opens a modal)
• Canceling zeros when dividing (Opens a modal)
• Divide multiples of 10, 100, and 1,000 by 1-digit numbers 7 questions Practice
• Cancel zeros when dividing 7 questions Practice

Division: place value and area

• Division using place value (Opens a modal)
• Division with area models (Opens a modal)
• Divide using place value 4 questions Practice
• Divide by 1-digit numbers with area models 4 questions Practice

Multi-digit division (no remainders)

• Intro to long division (no remainders) (Opens a modal)
• Long division: 280÷5 (Opens a modal)
• Divide multi-digit numbers by 2, 3, 4, and 5 (remainders) 7 questions Practice
• Zeros in the dividend (no remainders) 4 questions Practice
• Zeros in the quotient (no remainders) 4 questions Practice
• Intro to remainders (Opens a modal)
• Understanding remainders (Opens a modal)
• Interpreting remainders (Opens a modal)
• Long division with remainders: 3771÷8 (Opens a modal)
• Long division with remainders: 2292÷4 (Opens a modal)
• Divide with remainders (2-digit by 1-digit) 4 questions Practice
• Divide multi-digit numbers by 6, 7, 8, and 9 (remainders) 4 questions Practice
• Multi-digit division 4 questions Practice

Multi-digit division (remainders)

• Intro to long division (remainders) (Opens a modal)
• Dividing by 2-digits: 6250÷25 (Opens a modal)
• Dividing by 2-digits: 9815÷65 (Opens a modal)
• Dividing by 2-digits: 7182÷42 (Opens a modal)
• Partial quotient method of division: introduction (Opens a modal)
• Partial quotient method of division: example using very large numbers (Opens a modal)
• Divide by taking out factors of 10 4 questions Practice
• Basic multi-digit division 7 questions Practice
• Division by 2-digits 4 questions Practice

Multiplication and division word problems

• Multiplication word problem: carrots (Opens a modal)
• Division word problem: row boat (Opens a modal)
• Multiplication word problem: pizza (Opens a modal)
• Division word problem: field goals (Opens a modal)
• Multiplication, division word problem: pedaling (Opens a modal)
• Multiplication and division word problems 7 questions Practice
• Multi-step word problems with whole numbers 4 questions Practice

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons

Margin Size

• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

1.3.2: Dividing Whole Numbers and Applications

• Last updated
• Save as PDF
• Page ID 60897

• The NROC Project

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

Learning Objectives

• Use three different ways to represent division.
• Divide whole numbers.
• Perform long division.
• Divide whole numbers by a power of 10.
• Recognize that division by 0 is not defined.
• Solve application problems using division.

Introduction

Some people think about division as “fair sharing” because when you divide a number you are trying to create equal parts. Division is also the inverse operation of multiplication because it “undoes” multiplication. In multiplication, you combine equal sets to create a total. In division, you separate a whole group into sets that have the same amount. For example, you could use division to determine how to share 40 empanadas among 12 guests at a party.

What is Division?

Division is splitting into equal parts or groups. For example, one might use division to determine how to share a plate of cookies evenly among a group. If there are 15 cookies to be shared among five people, you could divide 15 by 5 to find the “fair share” that each person would get. Consider the picture below.

15 cookies split evenly across 5 plates results in 3 cookies on each plate. You could represent this situation with the equation:

\(\ 15 \div 5=3\)

You could also use a number line to model this division. Just as you can think of multiplication as repeated addition, you can think of division as repeated subtraction. Consider how many jumps you take by 5s as you move from 15 back to 0 on the number line.

Notice that there are 3 jumps that you make when you skip count by 5 from 15 back to 0 on the number line. This is like subtracting 5 from 15 three times. This repeated subtraction can be represented by the equation: \(\ 15 \div 5=3\).

Finally, consider how an area model can show this division. Ask yourself, if you were to make a rectangle that contained 15 squares with 5 squares in a row, how many rows would there be in the rectangle? Start by making one row of 5 squares:

Then add two more rows of 5 squares so you have 15 squares.

The number of rows is 3. So, 15 divided by 5 is equal to 3.

Find \(\ 24 \div 3\) using a set model and a number line model.

Number line model:

\(\ 24 \div 3=8\)

Ways to Represent Division

As with multiplication, division can be written using a few different symbols. We showed this division written as \(\ 15 \div 5=3\), but it can also be written two other ways:

\(\ \begin{array}{r} 3\\ 5 \longdiv { 1 5 } \end{array}\)

\(\ \frac{15}{5}=3\)

Each part of a division problem has a name. The number that is being divided up, that is the total, is called the dividend . In the work in this topic, this number will be the larger number, but that is not always true in mathematics. The number that is dividing the dividend is called the divisor . The answer to a division problem is called the quotient .

The blue box below summarizes the terminology and common ways to represent division.

Three Ways to Represent Division

\(\ 12 \div 3=4\) ( with a division symbol ; this equation is read "12 divided by 3 equals 4."

\(\ \begin{array}{r} 4\\ 3 \longdiv { 1 2 } \end{array}\) ( with a division or long division symbol ; this expression is read "12 divided by 3 equals 4." Notice here, though, that you have to start with what is underneath the symbol. This may take some getting used to since you are reading from right to left and bottom to top!)

\(\ \frac{12}{3}=4\) ( with a fraction bar ; this expression can also be read "12 divided by 3 equals 4." In this format, you read from top to bottom.)

In the examples above, 12 is the dividend , 3 is the divisor and 4 is the quotient.

\(\ \text { Dividend } \div \text { Divisor }=\text { Quotient }\)

\(\ \begin{array}{r} \text{Quotient}\\ \text{Divisor}\longdiv{\text{Dividend}} \end{array}\)

\(\ \frac{\text { Dividend }}{\text { Divisor }}=\text { Quotient }\)

Which of the following expressions represent dividing $56 equally among 7 people?

#1: \(\ \frac{7}{56}\)

#2: \(\ 56 \div 7\)

#3: \(\ 56\longdiv {7}\)

• #2 represents the situation.
• All three expressions represent the situation.
• #1 represents the situation.
• #3 represents the situation.
• Correct. #2 is the only expression that represents 56 divided by 7.
• Incorrect. #1 and #3 represent 7 divided by 56, not 56 divided by 7. The correct answer is #2 is the only expression that represents the situation.
• Incorrect. This expression represents 7 divided by 56, not 56 divided by 7. The correct answer is #2 is the only expression that represents the situation.

Dividing Whole Numbers

Once you understand how division is written, you are on your way to solving simple division problems. You will need your multiplication facts to perform division. If you do not have them memorized, you can guess and check or use a calculator.

Consider the following problems:

\(\ 10 \div 5=?\)

\(\ 48 \div 2=?\)

\(\ 30 \div 5=?\)

In the first problem, \(\ 10 \div 5\), you could ask yourself, “how many fives are there in ten?” You can probably answer this easily. Another way to think of this is to consider breaking up 10 into 5 groups and picturing how many would be in each group.

\(\ 10 \div 5=2\)

To solve \(\ 48 \div 2\), you might realize that dividing by 2 is like splitting into two groups or splitting the total in half. What number could you double to get 48?

\(\ 48 \div 2=24\)

To figure out \(\ 30 \div 5\), you could ask yourself, how many times do you have to skip count by 5 to get from 0 to 30? 5, 10, 15, 20, 25, 30. You have to skip count 6 times to get to 30.

\(\ 30 \div 5=6\)

Compute \(\ 35 \div 5\).

Compute \(\ 32 \div 4\).

Sometimes when you are dividing, you cannot easily share the number equally. Think about the division problem \(\ 9 \div 2\). You could think of this problem as 9 pieces of chocolate being split between 2 people. You could make two groups of 4 chocolates, and you would have one chocolate left over.

In mathematics, this left over part is called the remainder . It is the part that remains after performing the division. In the example above, the remainder is 1. We can write this as:

\(\ 9 \div 2=4\quad \mathrm{R} 1\)

We read this equation: “Nine divided by two equals four with a remainder of 1."

You might be thinking you could split that extra piece of chocolate in parts to share it. This is great thinking! If you split the chocolate in half, you could give each person another half of a piece of chocolate. They would each get \(\ 4 \frac{1}{2}\) pieces of chocolate. We are not going to worry about expressing remainders as fractions or decimals right now. We are going to use the remainder notation with the letter R. Here’s an example:

\(\ 45 \div 6\)

\(\ 45 \div 6=7\quad \mathrm{R} 3\)

Since multiplication is the inverse of division, you can check your answer to a division problem with multiplication. To check the answer 7 R3, first multiply 6 by 7 and then add 3.

\(\ 6 \cdot 7=42\)

\(\ 42+3=45\), so the quotient 7 R3 is correct.

Compute \(\ 67 \div 7\).

• Incorrect. \(\ 9 \cdot 7=63\). There is a remainder of 4. The correct answer is 9 R4.
• Correct. \(\ 9 \cdot 7=63\) and there are 4 left over.
• Incorrect. This is a division, not subtraction, problem. The correct answer is 9 R4.
• Incorrect. \(\ 70 \div 7=10\), so the answer to \(\ 67 \div 7\) cannot be; \(\ 9 \cdot 7=63\) and there are 4 left over. The correct answer is 9 R4.

Performing Long Division

Long division is a method that is helpful when you are performing division that you cannot do easily in your head, such as division involving larger numbers. Below is an example of a way to write out the division steps.

\(\ 68 \div 4\)

\(\ 68 \div 4=17\)

\(\ 6,707 \div 233\)

\(\ 6,707 \div 233=28 \quad\mathrm{R} 183\)

Compute \(\ 417 \div 34\).

• Incorrect. This is a division problem, not an addition problem. The correct answer is 12 R9.
• Incorrect. \(\ 12 \cdot 34=408\). The correct answer is 12 R9.
• Correct. \(\ 12 \cdot 34=408\) and \(\ 408+9=417\)
• Incorrect. \(\ 13 \cdot 34=442\). The correct answer is 12 R9.

Dividing Whole Numbers by a Power of 10

Just as multiplication by powers of 10 results in a pattern, there is a pattern with division by powers of 10. Consider three quotients: \(\ 20 \div 10 ; 200 \div 10 ; 2,000 \div 10\).

Think about \(\ 20 \div 10\). There are 2 tens in twenty, so \(\ 20 \div 10=2\). The computations for \(\ 200 \div 10\) and \(\ 2,000 \div 10\) are shown below.

\(\ 200 \div 10\)

\(\ 200 \div 10=20\)

\(\ 2000 \div 10\)

\(\ 2,000 \div 10=200\)

Examine the results of these three problems to try to determine a pattern in division by 10.

\(\ \begin{aligned} 20 \div 10 &=2 \\ 200 \div 10 &=20 \\ 2,000 \div 10 &=200 \end{aligned}\)

Notice that the number of zeros in the quotient decreases when a dividend is divided by 10: 20 becomes 2; 200 becomes 20 and 2,000 become 200. In each of the examples above, you can see that there is one fewer 0 in the quotient than there was in the dividend.

Continue another example of division by a power of 10.

\(\ 2,000 \div 100\)

\(\ 2,000 \div 100=20\)

Consider this set of examples of division by powers of 10. What pattern do you see?

\(\ \begin{array}{rl} 20 &\div &10=2 \\ 200 &\div &10=20 \\ 2,000 &\div &10=200 \\ 2,000 &\div &100=20 \\ 2,000 &\div &1,000=2 \end{array}\)

Notice that when you divide a number by a power of 10, the quotient has fewer zeros. This is because division by a power of 10 has an effect on the place value. For example, when you perform the division \(\ 18,000 \div 100=180\), the quotient, 180, has two fewer zeros than the dividend, 18,000. This is because the power of 10 divisor, 100, has two zeros.

Compute \(\ 135,000 \div 100\).

• Incorrect. This answer is too large. \(\ 13,500 \cdot 100=1,350,000\). The correct answer is 1,350.
• Incorrect. This is a division, not a subtraction, problem. The correct answer is 1,350.
• Incorrect. This is a division, not a multiplication, problem. The correct answer is 1,350.
• Correct. 1,350 \cdot 100=135,000.

Division by Zero

You know what it means to divide by 2 or divide by 10, but what does it mean to divide a quantity by 0? Is this even possible? Can you divide 0 by a number? Consider the two problems written below.

\(\ \frac{0}{8} \text { and } \frac{8}{0}\)

We can read the first expression, “zero divided by eight” and the second expression, “eight divided by zero.” Since multiplication is the inverse of division, we could rewrite these as multiplication problems.

\(\ 0 \div 8=?\)

\(\ ? \cdot 8=0\)

The quotient must be 0 because \(\ 0 \cdot 8=0\).

\(\ \frac{0}{8}=0\)

Now let’s consider \(\ \frac{8}{0}\).

\(\ 8 \div 0=?\)

\(\ ? \cdot 0=8\)

This is not possible. There is no number that you could multiply by zero and get eight. Any number multiplied by zero is always zero. There is no quotient for \(\ \frac{8}{0}\). There is no quotient for any number when it is divided by zero.

Division by zero is an operation for which you cannot find an answer, so it is not allowed. We say that division by 0 is undefined.

Using Division in Problem Solving

Division is used in solving many types of problems. Below are three examples from real life that use division in their solutions.

Luana made 40 empanadas for a party. If the empanadas are divided equally among 12 guests, how many will each guest have? Will there be any leftover empanadas?

Each guest will have 3 empanadas. There will be 4 empanadas left over.

A case of floor tiles has 12 boxes in it. The case costs $384. How much does one box cost?

Each box of tiles costs $32

A banana grower is shipping 4,644 bananas. There are 86 crates, each containing the same number of bananas. How many bananas are in each crate?

Each crate contains 54 bananas.

A theater has 1,440 seats. The theater has 30 rows of seats. How many seats are in each row?

• Incorrect. This answer is too large. Use division, \(\ 1440 \div 30\), not subtraction for this problem. The correct answer is 48.
• Correct. \(\ 1440 \div 30=48\).
• Incorrect. The answer is too large. Use division, \(\ 1440 \div 30\), not multiplication, for this problem. The correct answer is 48.
• Incorrect. There is a place-value error. The correct answer is 48.

Division is the inverse operation of multiplication, and can be used to determine how to evenly share a quantity among a group. Division can be written in three different ways: using a fraction bar, using a division symbol, and using long division. Division can be represented as splitting a total quantity into sets of equal quantities, as skip subtracting on the number line, and as a dimension with an area model. Remainders may result when performing division and they can be represented with the letter R, followed by the number remaining. Since division is the inverse operation of multiplication, you need to know your multiplication facts in order to do division. For larger numbers, you can use long division to find the quotient.